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Model predictive control (MPC) is a powerful tool for controlling complex nonlinear systems under constraints, but often struggles with model uncertainties and the design of suitable cost functions. To address these challenges, we discuss…

The three most common school choice mechanisms are the Deferred Acceptance mechanism (DA), the classic Boston mechanism (BM), and a variant of the Boston mechanism where students automatically skip exhausted schools, which we call the…

Ambition and risk-taking have been heralded as important ways for marginalized communities to get out of cycles of poverty. As a result, educational messaging often encourages individuals to strengthen their personal resolve and develop…

We study optimality for the safety-constrained Markov decision process which is the underlying framework for safe reinforcement learning. Specifically, we consider a constrained Markov decision process (with finite states and finite…

Tandem queueing systems are widely-used stochastic models that arise from many real-life service operations systems. Motivated by the desire to understand the trade-off between the performance and complexity of policies for…

A unified thermodynamic formalism describing the efficiency of learning is proposed. First, we derive an inequality, which is more strength than Clausius's inequality, revealing the lower bound of the entropy-production rate of a subsystem.…

Sampling-based Model Predictive Control (MPC) is a flexible control framework that can reason about non-smooth dynamics and cost functions. Recently, significant work has focused on the use of machine learning to improve the performance of…

With the integration of large-scale renewable energy sources to power systems, many optimization methods have been applied to solve the stochastic/uncertain transmission-constrained unit commitment (TCUC) problem. Among all methods,…

Barter exchange studies the setting where each agent owns a good, and they can exchange with each other if that gives them more preferred goods. This exchange will give better outcomes if there are more participants. The challenge here is…

Test-time scaling (TTS) has been shown to improve the performance of large language models (LLMs) by sampling and aggregating diverse reasoning paths. However, existing research has overlooked a critical issue: selection bias of reasoning…

We consider an expected-value ranking and selection (R&S) problem where all k solutions' simulation outputs depend on a common parameter whose uncertainty can be modeled by a distribution. We define the most probable best (MPB) to be the…

Meta-learning methods have shown an impressive ability to train models that rapidly learn new tasks. However, these methods only aim to perform well in expectation over tasks coming from some particular distribution that is typically…

This work is focused on optimal control of mechanical compression refrigeration systems. A reduced-order state-space model based on the moving boundary approach is proposed for the canonical cycle, which eases the controller design. The…

Markov chains are the de facto finite-state model for stochastic dynamical systems, and Markov decision processes (MDPs) extend Markov chains by incorporating non-deterministic behaviors. Given an MDP and rewards on states, a classical…

Queueing systems are widely applicable stochastic models with use cases in communication networks, healthcare, service systems, etc. Although their optimal control has been extensively studied, most existing approaches assume perfect…

We study the optimal investment problem for a continuous time incomplete market model such that the risk-free rate, the appreciation rates and the volatility of the stocks are all random; they are assumed to be independent from the driving…

Constrained reinforcement learning is to maximize the expected reward subject to constraints on utilities/costs. However, the training environment may not be the same as the test one, due to, e.g., modeling error, adversarial attack,…

As artificial agents become increasingly capable, what internal structure is *necessary* for an agent to act competently under uncertainty? Classical results show that optimal control can be *implemented* using belief states or world…

The existing literature on optimal auctions focuses on optimizing the expected revenue of the seller, and is appropriate for risk-neutral sellers. In this paper, we identify good mechanisms for risk-averse sellers. As is standard in the…

We study a memory-based Boolean game (MBBG) taking place on the regular ring, wherein each agent acts according to its local optimal states of the last M time steps recorded in memory, and the agents in the minority are rewarded. One free…